Mount Stuart was the son of the John Stuart, 1st Marquess of Bute and the grandson of Prime Minister John Stuart, 3rd Earl of Bute. His mother was the Hon. Charlotte Jane, daughter and heiress of Herbert Windsor, 2nd Viscount Windsor. He was born at Grosvenor Square, London in 1767 and educated at Eton and St John's College, Cambridge.
In 1790, he was elected Member of Parliament for Cardiff, a seat he held until his death. He was appointed Colonel of the Glamorganshire Militia in 1791 and was also Lord-Lieutenant of Glamorganshire between 1793 and his death.
Lord Mount Stuart married Lady Elizabeth McDouall-Crichton, daughter of Patrick McDouall-Crichton, 6th Earl of Dumfries, and his wife Margaret (née Crauford), on 12 October 1792. They had two sons, who both added the surname "Crichton" before that of "Stuart" in 1805:
Lord Mount Stuart died at Bassingbourn Hall near Stansted, Essex, in January 1794, only 26 years of age, a month after being injured in a fall from his horse. Lady Mount Stuart survived him by three years and died in July 1797, aged 24.